Computer simulation is carried out for the process of formation of electrohydrodynamic flows emerging in a system of two parallel wires as a result of symmetric injection from each electrode (2D case). Simulation is performed using the ANSYS system. A simulation algorithm is developed for nonstationary electrohydrodynamic flows. The results of simulation are presented. Analysis of the results shows that the evolution of electrohydrodynamic flows is accompanied by the formation of thin oppositely charged liquid streams moving in opposite direction from near-electrode charged layers.